According to our current understanding of physics, there are fundamental limitations that prevent objects with mass from reaching or exceeding the speed of light. These limitations arise from Einstein's theory of relativity, particularly the theory of special relativity.
As an object with mass accelerates, its relativistic mass increases, and the amount of energy required to continue accelerating it further also increases. As an object approaches the speed of light, its relativistic mass becomes infinitely large, and the energy required to accelerate it further would also become infinite. This means that it would take an infinite amount of energy to reach the speed of light, which is not feasible.
Additionally, as an object accelerates, its apparent mass increases, which leads to an increase in the object's inertia. This increase in inertia makes it harder to accelerate the object further, requiring increasingly larger amounts of thrust to achieve smaller increases in velocity. This effect is known as mass dilation.
Furthermore, as an object with mass approaches the speed of light, time dilation occurs. Time dilation means that time appears to pass more slowly for the object in motion relative to an observer at rest. This effect also contributes to the difficulty of reaching the speed of light, as it would require an infinite amount of time from the perspective of the object with mass.
Therefore, even with unlimited fuel and thrust, it is not possible for an object with mass, such as a spaceship, to continuously accelerate to or beyond the speed of light due to the limitations imposed by special relativity.